Up to now, certain filter materials have been produced in the form of filter foils, either by electrodepositing metal on lithographically structured matrices, or by partially covering metal foils with resist films and etching them. With both methods, a decrease in the dimensions of the filter apertures necessitates a smaller thickness of the filter foils. As a general rule of thumb, the thickness of the foil cannot be much larger than the width of the filter apertures. As a result, in the case of very small apertures, e.g., less than 50 micrometers, the foils are so thin that they are difficult to manipulate and will no longer resist mechanical loads. An additional disadvantage of the known production methods is that the open filter area decreases markedly in the case of filters having small filter apertures. Moreover, there is a large variation in the aperture width of such filters having small filter apertures. For example, in the case of filter apertures as few as 10 micrometers, the aperture width tolerance may be a multiple of the nominal width. In cases where such wide variations in the aperture width are not permissible, the filter foils have to be produced by more complicated methods such as by a combination of X-ray lithography and galvanization.